The survey was made on the recent researches of Internet congestion control,exploring mainly the fairness,stability and scalability of the congestion control schemes in the framework of duality model theory,according to several diverse clues of the development of these schemes.

The positive definite geometric programming is transferred into a nolinear programming with constraints of linear equality by duality principle.

Self-Insurance,Self-Protection and Market Insurance within the Dual Theory of Choice;

According to the dual theory,a simple geometric programming was proposed to derive a corresponding geometric dual problem instead of cross-entropy optimization problem with cross-entropy constraints,which is a concave programming one with linear constrains,leading to a simpler calculation.

In this paper, a new Hopfields-type neural network for linear programming, which is based on dual theory and makes use of Sigmoid function, is presented.

An Application of Duality Theory to The Analysis of Economic Equlilbrium;

This paper discuses the relationship between the saddle point of Lagrange function and the optimization solving of the primal optimization problem and its dual problem,with verification of some new features in duality theory.

Discuss the relations between the quadratic semi-definite programming and the semi-definite least squares problem,and study the primal-dual interior point algorithm for this programing based on the duality theory,and give the proof of the unique solution based on the NT search direction.